Question

A variable circle passes through the point A(2,1) and touches the x-axis . Locus of the other end of the diameter through A is is a parabola .
The two tangents and two normals at the extremities of the latus rectum of the parabola contitutes a quadrilateral . Find area of quadrilateral.

Answer 1

We have,

Point $(2,1)$ passes through the circle

Then, touches the X-axis So,

$Radiusofcircle=Abssicissa$

$r=2$

So the diameter

$=2\times raidus$

$=2\times 2=4$

So,

Tangents=Normals=2unit

So, Area of quadrilateral =$Length\times Breadth$

Area=$2\times =sq.units$

Hence, this is the answer.